Singularities of the hele-shaw flow and shock waves in dispersive media

Eldad Bettelheim, Oded Agam, Anton Zabrodin, Paul Wiegmann

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Kortevegâ€"de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.

Original languageEnglish
Article number244504
JournalPhysical Review Letters
Volume95
Issue number24
DOIs
Publication statusPublished - 9 Dec 2005
Externally publishedYes

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